Problem: Simplify the following expression: $ z = \dfrac{3}{10} - \dfrac{-4k}{k + 7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k + 7}{k + 7}$ $ \dfrac{3}{10} \times \dfrac{k + 7}{k + 7} = \dfrac{3k + 21}{10k + 70} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-4k}{k + 7} \times \dfrac{10}{10} = \dfrac{-40k}{10k + 70} $ Therefore $ z = \dfrac{3k + 21}{10k + 70} - \dfrac{-40k}{10k + 70} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{3k + 21 + 40k }{10k + 70} $ Distribute the negative sign: $z = \dfrac{3k + 21 + 40k}{10k + 70}$ $z = \dfrac{43k + 21}{10k + 70}$